Partition function zeros of the Q-state Potts model for non-integer Q

TL;DR

This study analyzes the distribution of Fisher zeros in the complex temperature plane for the two-dimensional Q-state Potts model with non-integer Q, revealing zero distributions and verifying key conjectures for ferromagnetic and antiferromagnetic cases.

Contribution

It provides new insights into Fisher zero distributions for non-integer Q and verifies the den Nijs and Baxter conjectures in this context.

Findings

Fisher zeros do not lie on the unit circle for Q<1.

Some Fisher zeros lie on the unit circle for Q>1, increasing with Q.

Verification of the den Nijs formula and Baxter conjecture for specific Q ranges.

Abstract

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On $L\times L$ self-dual lattices studied ($L\le8$), no Fisher zero lies on the unit circle $p_0=e^{i\theta}$ in the complex $p=(e^{\beta J}-1)/\sqrt{Q}$ plane for Q<1, while some of the Fisher zeros lie on the unit circle for Q>1 and the number of such zeros increases with increasing Q. The ferromagnetic and antiferromagnetic properties of the Potts model are investigated using the distribution of the Fisher zeros. For the Potts ferromagnet we verify the den Nijs formula for the thermal exponent $y_t$. For the Potts antiferromagnet we also verify the Baxter conjecture for the critical temperature and present new results for the thermal exponents in the range 0<Q<3.